Problem: Simplify; express your answer in exponential form. Assume $t\neq 0, p\neq 0$. $\dfrac{{(t^{-5})^{-1}}}{{(t^{5}p^{-1})^{2}}}$
Explanation: To start, try working on the numerator and the denominator independently. In the numerator, we have ${t^{-5}}$ to the exponent ${-1}$ . Now ${-5 \times -1 = 5}$ , so ${(t^{-5})^{-1} = t^{5}}$ In the denominator, we can use the distributive property of exponents. ${(t^{5}p^{-1})^{2} = (t^{5})^{2}(p^{-1})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(t^{-5})^{-1}}}{{(t^{5}p^{-1})^{2}}} = \dfrac{{t^{5}}}{{t^{10}p^{-2}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{5}}}{{t^{10}p^{-2}}} = \dfrac{{t^{5}}}{{t^{10}}} \cdot \dfrac{{1}}{{p^{-2}}} = t^{{5} - {10}} \cdot p^{- {(-2)}} = t^{-5}p^{2}$.